You said America is a theistic nation. I think the mention of gods (or lack thereof) in the establishing document of the US government is entirely relevant here.

You may as well mention the lack of direct mention of gods in the sentencing for tax evasion.

First, you're quoting the Declaration of Independence. This was simply a declaration of colonial separation, and is not the document that established basic human rights.

There's no 'establishing' basic human rights on the American view, and certainly not by any document. That's rather the point, yeah?

There is nothing about inalienable rights that is exclusive to theism. They can be attributed to a "creator", as in the Declaration of Independence, but many Enlightenment thinkers did not mention a creator in their explanations of this concept, and credited simply nature.

The American ones, didn't. They credited the Creator - as did, by the by, many Enlightenment thinkers. The atheists' prominence came along later, right around the time beheadings became all the rage.

If you wish to argue that there are certain rights woven into the very fabric of nature, rather than created by man, feel free. You'll not only be taking a minority view - which is quite fine - but you'll be taking on a metaphysical view which is utterly in opposition to materialism. Hello, fundamental teleology. Goodbye, atheism as the vast majority of modern proponents know it. At that point it's hard to distinguish the result from pantheism and panentheism.

The primary emphasis is that people are born with these rights. Keep in mind that several of the Founders were deists, which was often defined as a religion of nature.

Which is exactly why I'm saying America is a theist, but not a Christian, nation. Team Deism is on the theist side, and it's only defined as a 'religion of nature' insofar as observation of nature is regarded as pointing at God's existence.